Question9. $0.5(s-1)=2+s$ $s=\square$

Studdy Solution

STEP 1

1. The equation $0.5(s-1) = 2 + s$ is a linear equation in one variable, $s$ .
2. The goal is to solve for $s$ by isolating it on one side of the equation.
3. Basic algebraic operations such as distribution, combining like terms, and isolating the variable will be used.

STEP 2

1. Distribute the constant on the left side of the equation.
2. Simplify both sides of the equation.
3. Isolate the variable $s$ to find its value.
4. Check the solution by substituting it back into the original equation.

STEP 3

Distribute the $0.5$ on the left side of the equation:
$0.5(s - 1) = 0.5s - 0.5$
So the equation becomes:
$0.5s - 0.5 = 2 + s$

STEP 4

We need to get all terms involving $s$ on one side and constant terms on the other side.
Subtract $0.5s$ from both sides:
$0.5s - 0.5 - 0.5s = 2 + s - 0.5s$
This simplifies to:
$-0.5 = 2 + 0.5s$

STEP 5

Subtract 2 from both sides to isolate the term with $s$ :
$-0.5 - 2 = 0.5s$
Simplify the left side:
$-2.5 = 0.5s$
Now, divide both sides by $0.5$ to solve for $s$ :
$s = \frac{-2.5}{0.5}$
Simplify the division:
$s = -5$

STEP 6

Check the solution by substituting $s = -5$ back into the original equation:
Original equation:
$0.5(s - 1) = 2 + s$
Substitute $s = -5$ :
$0.5(-5 - 1) = 2 + (-5)$
Simplify both sides:
$0.5(-6) = -3$
$-3 = -3$
Both sides are equal, confirming the solution is correct.
The solution is:
$s = \boxed{-5}$

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